"We will impose Iraqi law in the entire region of Kurdistan under the constitution," he said.

Pressure has been mounting on the Kurds since the vote, not just from Baghdad but also from Ankara, with Turkey threatening a range of measures including cutting off export routes for the region.

An overwhelming "yes" vote had been widely expected.

Pursuing a long-cherished dream of statehood, the Kurds went ahead with the referendum in defiance of widespread objections, including from the UN and the US.

It has raised fears of unrest and the possibility of a military confrontation involving the Kurds, who are key allies in internationally backed offensives against the jihadists of the Islamic State (IS) group.

In a televised address late on Tuesday, Barzani had urged Abadi "not to close the door to dialogue because it is dialogue that will solve problems".

"We assure the international community of our willingness to engage in dialogue with Baghdad," he said, insisting the referendum was not meant "to delimit the border [between Kurdistan and Iraq], nor to impose it de facto".

Baghdad has steadily pushed back against the vote. MPs on Wednesday passed a resolution calling on Abadi to "take all necessary measures to maintain Iraq’s unity", including by deploying security forces to disputed areas. The resolution also called for the closure of border posts with Turkey and Iran that are outside central government control.

Abadi said on Tuesday he would ban all international flights to and from Kurdistan in three days unless airports in its main cities, Arbil and Sulaymaniyah, were placed under his government’s control.

Lebanon’s Middle East Airlines and EgyptAir both said on Wednesday they would halt flights to Arbil this week at the request of Baghdad.

Turkey fears the vote will stoke the separatist ambitions of its own sizeable Kurdish minority and on Tuesday President Recep Tayyip Erdogan warned that Iraq’s Kurds risked sparking an "ethnic war".

"If Barzani and the Kurdistan Regional Government do not go back on this mistake as soon as possible, they will go down in history with the shame of having dragged the region into an ethnic and sectarian war," he said.

Erdogan had earlier warned that Turkey would shut its border with Iraqi Kurdistan and threatened to block oil exports from the region through Turkey.

Erdogan even suggested the possibility of a cross-border incursion similar to the one Turkey carried out against IS and Kurdish fighters in Syria.

Monday’s vote took place across the three northern provinces of autonomous Iraqi Kurdistan — Arbil, Sulaymaniyah and Dohuk — and in disputed border zones.